Numerical simulation of concentration field during the growth of single crystal Si in a cusp magnetic field

In order to control the size of crystal, the content of foreign metal impurities, the uniform distribution of oxygen and doped elements, a new crystal growth method, which is the combination of cusp magnetic field and Czochralski method, is proposed. Based on the physical and mathematical model for the growth system of Si crystal, the non-dimensional form treatment and find the solution the help of boundary condition established, a numerical simulation on concentration field in the melt and the crystal is investigated by using FDM (finite difference method) during the growth of Si single crystal in the cusp magnetic. Simulation results indicate that the use of cusp magnetic field in the growth of Si crystal enables to achieve the distribution uniformity of oxygen concentration in the crystal by controlling the concentration and distribution of oxygen element in the melt and at the solid-liquid interface through changing the density of magnetic field, rotating speed of the crystal and crucible, and radius of the crystal.